Problem: Omar is 20 years older than Umaima. Twenty years ago, Omar was 5 times as old as Umaima. How old is Umaima now?
Answer: We can use the given information to write down two equations that describe the ages of Omar and Umaima. Let Omar's current age be $o$ and Umaima's current age be $u$ The information in the first sentence can be expressed in the following equation: $o = u + 20$ Twenty years ago, Omar was $o - 20$ years old, and Umaima was $u - 20$ years old. The information in the second sentence can be expressed in the following equation: $o - 20 = 5(u - 20)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $u$ , it might be easiest to use our first equation for $o$ and substitute it into our second equation. Our first equation is: $o = u + 20$ . Substituting this into our second equation, we get the equation: $(u + 20)$ $-$ $20 = 5(u - 20)$ which combines the information about $u$ from both of our original equations. Simplifying both sides of this equation, we get: $u + 0 = 5 u - 100$ Solving for $u$ , we get: $4 u = 100$ $u = 25$.